39. Suppose initial margin rate is 50% and maintenance margin rate is 30%. You sell short some stock. What is the net return of the stock when you get the SECOND margin call? Note the answer for this question is the same regardless of the initial stock price. Express your answer as a decimal after rounding it to the nearest basis point. For example, type 0.2515 if your answer is 25.1533%. (Hint: We dont need new formulas for the second margin call. When you provide the extra collateral at the first margin call, everything is reset. So, it is like you are having a new short sale position at the first margin call. You know the stock price at the first margin call and you already met the initial margin condition. Therefore, the real second margin call in this question is nothing but another first margin call after the real first margin call. So, you can use the same formula in the lecture note to find the return at the real second margin call by compounding two returns for the period before the first margin call and the period between the first and the second margin call.)

44. Suppose the current stock price is $120 and the stock price in a year can be either $150 or $100. The risk-free rate is 2% per year, compounded annually. Compute the price of a European put option that expires in a year. The strike price is K=$130. Type your answer without $ as a numerical value and round the number to the nearest hundredth. For example, type 34.27 if you think the answer is $34.265. (Hint: This is a put option case, not a call option. Be careful when you compute the cash-flow at expiration date. All other calculations should be the same as call option case.)

49. Last month, you found the tangency portfolio and constructed your optimal complete portfolio, which is a mix of the tangency portfolio and the risk-free asset. Today new information about the stock market is released and affects the moments (mean, variance, and covariance) of all stock returns. You update your belief on the moments, find the new tangency portfolio, and re-construct your optimal complete portfolio, given new information. The risk premium of the updated tangency portfolio is 1.42 times the previous one, and the volatility of the updated tangency portfolio is 1.2 times the previous one due to the new information. If the weight on the tangency portfolio was 0.6 and 0.4 on the risk-free asset in your previous optimal complete portfolio, what is the weight on the updated tangency portfolio in your re-constructed optimal complete portfolio? Assume your attitude to risk ( = price of risk) remains the same. Type your answer as a decimal after rounding the number to the nearest basis point. For example, type 0.2157 if you think the answer is 21.568%.